A bivariate INAR(1) model with different thinning parameters

A bivariate integer-valued autoregressive time series model of order one is introduced. Regression coefficients of the model are random variables so the interaction between processes is stochastic. The dependance is achieved through survival components which are based on the binomial thinning operator. General form of the model is considered where counting series, which determine the survival components, are generated by different binomial distributions. Due to a large number of parameters, generalized method of moments and conditional maximum likelihood methods are suggested for parameters estimation and their asymptotic properties are established. Possible application of the model is discussed on real data.